Koda, Yuya

写真a

Affiliation

Faculty of Economics (Hiyoshi)

Position

Professor

Related Websites

Contact Address

4-1-1, Hiyoshi, Kohoku, Yokohama, 223-8521, Japan
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Career 【 Display / hide 】

  • 2005.04
    -
    2007.09

    JSPS Reasearch Fellow, DC1

  • 2007.10
    -
    2008.03

    JSPS Reasearch Fellow, PD

  • 2008.04
    -
    2008.05

    Keio University, Department of Mathematics, Visiting Scholar

  • 2008.06
    -
    2008.09

    Kogakuin University, Academic Support Center, Lecturer

  • 2008.10
    -
    2009.08

    Tokyo Institute of Technology, Department of Mathematics, Assistant Professor

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Academic Background 【 Display / hide 】

  • 2000.04
    -
    2003.03

    Keio University, 理工学部, 数理科学科

    University, Graduated

  • 2003.04
    -
    2005.03

    Keio University, 大学院理工学研究科, 基礎理工学専攻

    Graduate School, Completed, Master's course

  • 2005.04
    -
    2007.09

    Keio University, 大学院理工学研究科, 基礎理工学専攻

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • Ph.D. (Science), Keio University, Coursework, 2007.09

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Papers 【 Display / hide 】

  • Positive flow-spines and contact 3-manifolds

    Ishii I., Ishikawa M., Koda Y., Naoe H.

    Annali di Matematica Pura ed Applicata (Annali di Matematica Pura ed Applicata)  202 ( 5 ) 2091 - 2126 2023.10

    ISSN  03733114

    　View Summary

    A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. It is known by Thurston and Winkelnkemper that any open book decomposition of a closed oriented 3-manifold supports a contact structure. In this paper, we introduce a notion of positivity for flow-spines and prove that any positive flow-spine of a closed, connected, oriented 3-manifold supports a contact structure uniquely up to isotopy. The positivity condition is critical to the existence of the unique, supported contact structure, which is also proved in the paper.

  • Homotopy Motions of Surfaces in 3-Manifolds

    Koda Y., Sakuma M.

    Quarterly Journal of Mathematics (Quarterly Journal of Mathematics)  74 ( 1 ) 29 - 71 2023.03

    ISSN  00335606

    　View Summary

    We introduce the concept of a homotopy motion of a subset in a manifold and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behavior of simple loops on a Heegaard surface and monodromies of virtual branched covering surface bundles associated with a Heegaard splitting.

  • Positive flow-spines and contact 3-manifolds, II

    Ishii I., Ishikawa M., Koda Y., Naoe H.

    Annali di Matematica Pura ed Applicata (Annali di Matematica Pura ed Applicata)   2023

    ISSN  03733114

    　View Summary

    In our previous paper, it is proved that for any positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique contact structure supported by P up to isotopy. In particular, this defines a map from the set of isotopy classes of positive flow-spines of M to the set of isotopy classes of contact structures on M. In this paper, we show that this map is surjective. As a corollary, we show that any flow-spine can be deformed to a positive flow-spine by applying first and second regular moves successively.

  • Four-manifolds with shadow-complexity one

    Yuya Koda, Bruno Martelli, Hironobu Naoe

    Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série 6 31 ( 4 ) 1111 - 1212 2022

    Research paper (scientific journal), Joint Work, Accepted

  • Braid group and leveling of a knot

    Sangbum Cho, Yuya Koda, Arim Seo

    Journal of Topology and Analysis (Journal of Topology and Analysis)  14 ( 4 ) 945 - 968 2022

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  17935253

    　View Summary

    Any knot K in genus-1 1-bridge position can be moved by isotopy to lie in a union of n parallel tori tubed by n - 1 tubes so that K intersects each tube in two spanning arcs, which we call a leveling of the position. The minimal n for which this is possible is an invariant of the position, called the level number. In this work, we describe the leveling by the braid group on two points in the torus, which yields a numerical invariant of the position, called the (1, 1)-length. We show that the (1, 1)-length equals the level number. We then find braid descriptions for (1,1)-positions of all 2-bridge knots providing upper bounds for their level numbers and also show that the (-2, 3, 7)-pretzel knot has level number two.

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • 3次元トポロジーに由来する写像類群の部分群の構造解明

    2024.04
    -
    2028.03

    基盤研究(C), Principal investigator

  • 多面体を用いた３・４次元多様体の微分構造と幾何構造の研究

    2021.04
    -
    Present

    文部科学省・日本学術振興会, 科学研究費補助金 基盤研究（C）, Principal investigator

  • 多面体を用いた３・４次元多様体の微分構造と幾何構造の研究

    2020.04
    -
    2024.03

    基盤研究(C), Principal investigator

  • ３次元多様体のシャドウ複雑度と幾何構造に関する研究

    2017.04
    -
    2021.03

    文部科学省・日本学術振興会, 科学研究費補助金 基盤研究（C）, Principal investigator

  • ヒーガード分解の写像類群の研究

    2014.04
    -
    2017.03

    文部科学省・日本学術振興会, 科学研究費補助金 若手研究（B）, Principal investigator

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Courses Taught 【 Display / hide 】

  • MATHEMATICS FOR ECONOMICS 2

    2024

  • MATHEMATICS FOR ECONOMICS 1

    2024

  • LINEAR ALGEBRA

    2024

  • INTRODUCTION TO CALCULUS

    2024

  • CALCULUS

    2024

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Memberships in Academic Societies 【 Display / hide 】

  • The Mathematical Society of Japan, 

    2006
    -
    Present
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Committee Experiences 【 Display / hide 】

  • 2024.03
    -
    Present

    Scientific Editor, Journal of Knot Theory and Its Ramifications

  • 2022.04
    -
    2023.03

    理学部数学科長, 広島大学

  • 2022.03
    -
    2023.02

    中国・四国支部 評議員, 日本数学会

  • 2020.04
    -
    2023.03

    Hiroshima Mathematical Journal 編集委員

  • 2016.06
    -
    2020.05

    雑誌『数学』 編集委員, 日本数学会

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